Chapter 14: Rates of Reaction Chemistry 1062: Principles of Chemistry II Andy Aspaas, Instructor

Chemical kinetics Study of the rate or speed of reactions Rate may be affected by any of the following: –Concentration of reactants –Presence or concentration of a catalyst –Temperature at which reaction occurs –Surface area of solid reactant or catalyst

Reaction rate Reaction rate can be defined in terms of appearance of product or disappearance of reactant Rates are given as a change in molar concentration in a certain time interval, unit mol/(L·s) For the reaction A + 2B  C, the rate of the reaction may be expressed 3 ways

Dependence of rate on concentration Reaction rate usually depends on the concentrations of reactants and catalysts Rate law shows this dependence For the reaction a A + b B  d D + e E (reactants A and B form D and E with catalyst C) Rate = k [A] m [B] n [C] p where m, n, and p are exponents, usually integers m, n, and p must be detemined experimentally! C

Reaction order The reaction order can be given with respect to a certain reactant, or overall –For a certain reactant, it’s the exponent in the rate law –Overall, it’s the sum of the exponents Ex. 2NO(g) + 2H 2 (g)  N 2 (g) + 2H 2 O(g) Rate = k [NO] 2 [H 2 ] The reaction is second order in NO, first order in H 2, and third order overall.

Determining the rate law The method of initial rates is often used to determine the rate law and order of a reaction –Several experiments are run, varying the concentration of individual reactants and catalysts –The exponents in the rate law can be determined algebraically –The rate constant is determined by substituting the concentrations of any experiment into the rate law

Method of initial rates I – (aq) + ClO – (aq)  IO – (aq) + Cl – (aq) What is the rate law, and what is the rate constant, k? Concentrations are in mol/L, rates are in mol/(L·s) [I – ][ClO – ]OH – Rate Exp x Exp x Exp x Exp x OH –

Change of concentration writh time First order rate law for aA  products: Second-order rate law for aA  products:

Change of concentration with time Zero-order rate law for aA  products: Half life (t 1/2 ): time at which [A] t = -(1/2)[A] 0 (Reactant concentration is at 1/2 its initial value Radioactive decay, etc.

Graphing kinetic data While the method of initial rates is a quick way of determining reaction order, graphing the data is more effective Concentration of a reactant is measured in several time intervals throughout the reaction Integrated rate laws can be rearranged if necessary to y = mx + b format for graphing, where m is the slope and b is the y-intercept

Determination of reactant order by graphing Graph 3 times for the 3 rate laws, and determine which has a straight line Zero order: [A] vs. t is linear, slope = -k 1st order: ln[A] vs. t is linear, slope = -k 2nd order: 1/[A] vs. t is linear, slope = k

Rate dependence on temperature Collision theory: rate constant of a reaction is a factor of molecular collision frequency, activation energy, and the fraction of collisions which occur with a constructive orientation Activation energy: minimum molecular energy required in order for a collision to produce a reaction Transition-state theory: reactions must pass through an activated complex, an unstable grouping of atoms that has an equal chance of breaking into reactants or products

Potential energy diagrams Plot of potential energy (kJ/mol) vs. the course of a reaction (reactants becoming products by passing through an activated complex) NO + Cl 2  NOCl 2 ‡  NOCl + Cl + = = + ∆=

Arrhenius equation Rate constant of a chemical reaction is related to the activation energy and temperature A is a constant, based on collision frequency, and proper orientation, etc.

Elementary reactions A chemical reaction may consist of several steps in order to get from reactants to products Elementary reaction: a single molecular event, ex. the collision of molecules, or the separation of a molecule Reaction intermediate: species produced during a reaction that does not appear in the net equation (cancels out when elementary reactions are added) The order of a rate law for an elementary reaction can be predicted, but without knowledge of the mechanism, the rate law for an overall reaction cannot be predicted

Catalysis A catalyst increases the rate of a reaction but is not consumed Must be re-generated stiochiometrically in an elementary reaction Catalysts do not appear as a reactant or product in the overall reaction (shown above arrow) Work by reducing activation energy